Computer based navigation systems such as autonomous driving vehicles and mapping applications have created a need to acquire large area scans, photographs, and point cloud data sets (point cloud data sets include data sets obtained by remote sensing using infrared lasers, often called Light Detection And Ranging, or LiDAR). Large scale LiDAR scans (such as a scan of several city blocks) may be captured from either ground or aerial based mobile platforms. Despite the use of multi-band global positioning systems (GPS) and high-precision inertial measurement unit (IMU) with these systems, registration errors occur when aligning scans. Errors in misalignment and inaccurate registration can be as big as a few meters, even with the most accurate and expensive scanning equipment. Scans may additionally have non-rigid distortions; one example is a straight line appearing as curved in the scanned data. Non-linear distortions, which are typically caused by the scanner's internal drift, cannot be resolved by rigid transformation.
Current methods of resolving registration and deformation errors include iterative closest point (ICP) variants. ICP methods estimate a rigid transformation between two point clouds but fail to resolve non-rigid deformation and are thus inaccurate in aligning large-scale urban environment scans. ICP methods and ICP variants are further ineffective when ground truth or reference data for the point clouds are unavailable.